The 27-year-old, who could win his first Lions cap from the replacements bench in Melbourne, insists he and his team-mates have no intention of being taken to a deciding Test in Sydney next week. Instead, they have their hearts and minds set on creating history at the first attempt.
"There is an incredible focus in the squad. We want to win this series so badly," said Grant, who, along with Tommy Bowe, Sean O'Brien and Conor Murray, is one of four new faces in the matchday 23.
"I've never been in an environment that's more hungry for a win and more hungry to make history. The mood in the camp this week has been really positive. The boys are all pumped up and ready.
"We are locked away in camp so we don't really know what's happening back home, but we know the history and we know what's at stake on Saturday night. More importantly, we know what we need to do.
"We are so focused in terms of winning this Test series. I haven't thought about previous Tests but the chance to make history is at the back of your mind. We can make heroes of ourselves on Saturday. We're not out here to soak up the sun."
Grant only joined up with the squad as an injury replacement after Gethin Jenkins became the second loosehead to be ruled out of the tour while the Lions were in Perth but now he finds himself involved in the biggest game in the recent history of British & Irish rugby.
And playing his part this evening will mark an incredible journey the Glasgow Warriors prop, who was uncapped just over 12 months ago.
Grant only made his Scotland bow here in Australia in early June last year and was largely unheralded outside of his home nation until this season's RBS 6 Nations. A strong showing in the spring saw him tipped for a Lions berth but he missed out on selection, first to Jenkins, Cian Healy and Mako Vunipola, and then to fellow replacement Alex Corbisiero.
Grant didn't arrive in Australia until June 8 but he was almost immediately involved against a Combined Country XV three days later and, having tasted the emotional low of defeat to the Brumbies a week-and-a-half ago, he admits it's been one hell of a ride just to get to this point.
"It's a bit cheesy but it's like a dream come true for me. There are no other words to describe what has happened to me in the last few weeks," added Grant.
"Getting here was a bit of an adventure. I had to hit the ground running in a sense. I got here on the Saturday of the Reds game and I played on the Tuesday night, so it was pretty manic trying to learn the lineout calls. I had to meet everybody and get to know my team mates, it was a bit like being the new boy at school. Now it all feels natural.
"I used to play rugby in the garden with my dad and I wore a Lions shirt. I always said I wanted to play for Scotland and, having achieved that, the Lions was the next target. It's as high as you can go and when I told my fiancée Maxine that I had been selected she got pretty emotional.
"We found out the team on Wednesday night and I was half expecting it to be honest because I knew Alex (Corbisiero) was struggling a bit. It was great to get the win on Tuesday night and I thought the scrummaging went well so I hoped to make the squad. I hoped to be involved one way or another but it was nice to hear your name read out.
"Losing to the Brumbies was a really tough one to take and the boys involved in that match were determined to put things right against the Rebels in midweek. Losing with the Lions is far worse an experience than losing with any other side. You could see the disappointment in the squad: we went out to prove a point on Tuesday night and guys like myself now have a shot at the Test team."